On the efficiency of reductions in µ-SIMD media extensions

Many important multimedia applications contain a significant fraction of reduction operations. Although, in general, multimedia applications are characterized for having high amounts of Data Level Parallelism, reductions and accumulations are difficult to parallelize and show a poor tolerance to increases in the latency of the instructions. This is specially significant for µ-SIMD extensions such as MMX or AltiVec. To overcome the problem of reductions in µ-SIMD ISAs, designers tend to include more and more complex instructions able to deal with the most common forms of reductions in multimedia. As long as the number of processor pipeline stages grows, the number of cycles needed to execute these multimedia instructions increases with every processor generation, severely compromising performance. The paper presents an in-depth discussion of how reductions/accumulations are performed in current µ-SIMD architectures and evaluates the performance trade-offs for near-future highly aggressive superscalar processors with three different styles of µ-SIMD extensions. We compare a MMX-like alternative to a MDMX-like extension that has packed accumulators to attack the reduction problem, and we also compare it to MOM, a matrix register ISA. We show that while packed accumulators present several advantages, they introduce artificial recurrences that severely degrade performance for processors with high number of registers and long latency operations. On the other hand, the paper demonstrates that longer SIMD media extensions such as MOM can take great advantage of accumulators by exploiting the associative parallelism implicit in reductions.Peer ReviewedPostprint (published version

Streaming Reduction Circuit

Reduction circuits are used to reduce rows of floating point values to single values. Binary floating point operators often have deep pipelines, which may cause hazards when many consecutive rows have to be reduced. We present an algorithm by which any number of consecutive rows of arbitrary lengths can be reduced by a pipelined commutative and associative binary operator in an efficient manner. The algorithm is simple to implement, has a low latency, produces results in-order, and requires only small buffers. Besides, it uses only a single pipeline for the involved operation. The complexity of the algorithm depends on the depth of the pipeline, not on the length of the input rows. In this paper we discuss an implementation of this algorithm and we prove its correctness

AUTOMATING DATA-LAYOUT DECISIONS IN DOMAIN-SPECIFIC LANGUAGES

A long-standing challenge in High-Performance Computing (HPC) is the simultaneous achievement of programmer productivity and hardware computational efficiency. The challenge has been exacerbated by the onset of multi- and many-core CPUs and accelerators. Only a few expert programmers have been able to hand-code domain-specific data transformations and vectorization schemes needed to extract the best possible performance on such architectures. In this research, we examined the possibility of automating these methods by developing a Domain-Specific Language (DSL) framework. Our DSL approach extends C++14 by embedding into it a high-level data-parallel array language, and by using a domain-specific compiler to compile to hybrid-parallel code. We also implemented an array index-space transformation algebra within this high-level array language to manipulate array data-layouts and data-distributions. The compiler introduces a novel method for SIMD auto-vectorization based on array data-layouts. Our new auto-vectorization technique is shown to outperform the default auto-vectorization strategy by up to 40% for stencil computations. The compiler also automates distributed data movement with overlapping of local compute with remote data movement using polyhedral integer set analysis. Along with these main innovations, we developed a new technique using C++ template metaprogramming for developing embedded DSLs using C++. We also proposed a domain-specific compiler intermediate representation that simplifies data flow analysis of abstract DSL constructs. We evaluated our framework by constructing a DSL for the HPC grand-challenge domain of lattice quantum chromodynamics. Our DSL yielded performance gains of up to twice the flop rate over existing production C code for selected kernels. This gain in performance was obtained while using less than one-tenth the lines of code. The performance of this DSL was also competitive with the best hand-optimized and hand-vectorized code, and is an order of magnitude better than existing production DSLs.Doctor of Philosoph

On the scalability of 1- and 2-dimensional SIMD extensions for multimedia applications

SIMD extensions are the most common technique used in current processors for multimedia computing. In order to obtain more performance for emerging applications SIMD extensions need to be scaled. In this paper we perform a scalability analysis of SIMD extensions for multimedia applications. Scaling a 1-dimensional extension, like Intel MMX, was compared to scaling a 2-dimensional (matrix) extension. Evaluations have demonstrated that the 2-d architecture is able to use more parallel hardware than the 1-d extension. Speed-ups over a 2-way superscalar processor with MMX-like extension go up to 4X for kernels and up to 3.3X for complete applications and the matrix architecture can deliver, in some cases, more performance with simpler processor configurations. The experiments also show that the scaled matrix architecture is reaching the limits of the DLP available in the internal loops of common multimedia kernels.Peer ReviewedPostprint (published version

Energy-Efficient Computing for Mobile Signal Processing

Mobile devices have rapidly proliferated, and deployment of handheld devices continues to increase at a spectacular rate. As today's devices not only support advanced signal processing of wireless communication data but also provide rich sets of applications, contemporary mobile computing requires both demanding computation and efficiency. Most mobile processors combine general-purpose processors, digital signal processors, and hardwired application-specific integrated circuits to satisfy their high-performance and low-power requirements. However, such a heterogeneous platform is inefficient in area, power and programmability. Improving the efficiency of programmable mobile systems is a critical challenge and an active area of computer systems research. SIMD (single instruction multiple data) architectures are very effective for data-level-parallelism intense algorithms in mobile signal processing. However, new characteristics of advanced wireless/multimedia algorithms require architectural re-evaluation to achieve better energy efficiency. Therefore, fourth generation wireless protocol and high definition mobile video algorithms are analyzed to enhance a wide-SIMD architecture. The key enhancements include 1) programmable crossbar to support complex data alignment, 2) SIMD partitioning to support fine-grain SIMD computation, and 3) fused operation to support accelerating frequently used instruction pairs. Near-threshold computation has been attractive in low-power architecture research because it balances performance and power. To further improve energy efficiency in mobile computing, near-threshold computation is applied to a wide SIMD architecture. This proposed near-threshold wide SIMD architecture-Diet SODA-presents interesting architectural design decisions such as 1) very wide SIMD datapath to compensate for degraded performance induced by near-threshold computation and 2) scatter-gather data prefetcher to exploit large latency gap between memory and the SIMD datapath. Although near-threshold computation provides excellent energy efficiency, it suffers from increased delay variations. A systematic study of delay variations in near-threshold computing is performed and simple techniques-structural duplication and voltage/frequency margining-are explored to tolerate and mitigate the delay variations in near-threshold wide SIMD architectures. This dissertation analyzes representative wireless/multimedia mobile signal processing algorithms, proposes an energy-efficient programmable platform, and evaluates performance and power. A main theme of this dissertation is that the performance and efficiency of programmable embedded systems can be significantly improved with a combination of parallel SIMD and near-threshold computations.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86356/1/swseo_1.pd

Optimized Vectorization Implementation of CRYSTALS-Dilithium

CRYSTALS-Dilithium is a lattice-based signature scheme to be standardized by NIST as the primary post-quantum signature algorithm. In this work, we make a thorough study of optimizing the implementations of Dilithium by utilizing the Advanced Vector Extension (AVX) instructions, specifically AVX2 and the latest AVX512. We first present an improved parallel small polynomial multiplication with tailored early evaluation (PSPM-TEE) to further speed up the signing procedure, which results in a speedup of 5\%-6\% compared with the original PSPM Dilithium implementation. We then present a tailored reduction method that is simpler and faster than Montgomery reduction. Our optimized AVX2 implementation exhibits a speedup of 3\%-8\% compared with the state-of-the-art of Dilithium AVX2 software. Finally, for the first time, we propose a fully and highly vectorized implementation of Dilithium using AVX-512. This is achieved by carefully vectorizing most of Dilithium functions with the AVX512 instructions in order to improve efficiency both for time and for space simultaneously. With all the optimization efforts, our AVX-512 implementation improves the performance by 37.3\%/50.7\%/39.7\% in key generation, 34.1\%/37.1\%/42.7\% in signing, and 38.1\%/38.7\%/40.7\% in verification for the parameter sets of Dilithium2/3/5 respectively. To the best of our knowledge, our AVX512 implementation has the best performance for Dilithium on the Intel x64 CPU platform to date.Comment: 13 pages, 5 figure